OpenAI Embeddings & Cosine Similarity with Python

What Are Text Embeddings?

Text embeddings are numerical vector representations of text that capture semantic meaning. Sentences with similar meanings have vectors that point in similar directions in high-dimensional space. This makes embeddings incredibly powerful for search, recommendations, clustering, and classification tasks.

How It Works

Step 1: Setup & Imports

Start by importing the required libraries and loading your API key from a .env file:

from openai import OpenAI
from dotenv import load_dotenv
import os
import numpy as np

load_dotenv()

client = OpenAI(
    api_key=os.getenv("OPENAI_API_KEY")
)

Step 2: Define Your Sentences

Prepare the sentences you want to compare. We'll use three examples — two related to dogs, and one about databases:

sentences = [
    "I love dogs",
    "Dogs are wonderful pets",
    "SQL Server is a database"
]

Step 3: Generate Embeddings

Loop through each sentence and call the OpenAI Embeddings API using the text-embedding-3-small model:

vectors = []

for sentence in sentences:

    response = client.embeddings.create(
        model="text-embedding-3-small",
        input=sentence
    )

    vectors.append(response.data[0].embedding)

Step 4: Cosine Similarity Function

Define a function to compute the cosine similarity between two vectors. Cosine similarity ranges from -1 (opposite) to 1 (identical direction):

def cosine_similarity(a, b):
    a = np.array(a)
    b = np.array(b)

    return np.dot(a, b) / (
        np.linalg.norm(a) * np.linalg.norm(b)
    )

Step 5: Compare & Print Results

Compare the first sentence against the second and third to see how semantic similarity is reflected in the scores:

score1 = cosine_similarity(
    vectors[0],
    vectors[1]
)

score2 = cosine_similarity(
    vectors[0],
    vectors[2]
)

print("Dog vs Dog:", score1)
print("Dog vs Database:", score2)

Expected Output

Complete Code

Here's the complete script in one block — ready to run:

from openai import OpenAI
from dotenv import load_dotenv
import os
import numpy as np

load_dotenv()

client = OpenAI(
    api_key=os.getenv("OPENAI_API_KEY")
)

sentences = [
    "I love dogs",
    "Dogs are wonderful pets",
    "SQL Server is a database"
]

vectors = []

for sentence in sentences:

    response = client.embeddings.create(
        model="text-embedding-3-small",
        input=sentence
    )

    vectors.append(response.data[0].embedding)


def cosine_similarity(a, b):
    a = np.array(a)
    b = np.array(b)

    return np.dot(a, b) / (
        np.linalg.norm(a) * np.linalg.norm(b)
    )


score1 = cosine_similarity(
    vectors[0],
    vectors[1]
)

score2 = cosine_similarity(
    vectors[0],
    vectors[2]
)

print("Dog vs Dog:", score1)
print("Dog vs Database:", score2)

Dependencies

Install these packages before running the script:

pip install openai python-dotenv numpy

Real-World Use Cases

Text embeddings with cosine similarity power many AI applications:

• Semantic Search — Find documents that match the meaning of a query, not just keywords
• Recommendation Engines — Suggest similar products, articles, or content based on description similarity
• Document Clustering — Group similar documents together for organization or analysis
• Duplicate Detection — Identify near-duplicate content even with different wording
• Chatbot Memory — Retrieve the most relevant past conversation context

Next Steps

Now that you understand embeddings and similarity, take it further:

1. Build a semantic search engine over your own documents
2. Combine embeddings with a vector database like FAISS or ChromaDB
3. Implement RAG (Retrieval-Augmented Generation) to ground LLM responses in your data
4. Try text-embedding-3-large for higher-quality embeddings at a slightly higher cost